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Linear Regression Using Numpy

Giuseppe Vettigli user avatar by
Giuseppe Vettigli
·
Mar. 26, 12 · Interview
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A few posts ago, we saw how to use the function numpy.linalg.lstsq(...) to solve an over-determined system. This time, we'll use it to estimate the parameters of a regression line.

A linear regression line is of the form w1x+w2=y and it is the line that minimizes the sum of the squares of the distance from each data point to the line. So, given n pairs of data (xi, yi), the parameters that we are looking for are w1 and w2 which minimize the error



and we can compute the parameter vector w = (w1 , w2)T as the least-squares solution of the following over-determined system



Let's use numpy to compute the regression line:
from numpy import arange,array,ones,random,linalg
from pylab import plot,show

xi = arange(0,9)
A = array([ xi, ones(9)])
# linearly generated sequence
y = [19, 20, 20.5, 21.5, 22, 23, 23, 25.5, 24]
w = linalg.lstsq(A.T,y)[0] # obtaining the parameters

# plotting the line
line = w[0]*xi+w[1] # regression line
plot(xi,line,'r-',xi,y,'o')
show()
We can see the result in the plot below.



You can find more about data fitting using numpy in the following posts:

  • Polynomial curve fitting
  • Curve fitting using fmin
Linear regression NumPy

Published at DZone with permission of Giuseppe Vettigli, DZone MVB. See the original article here.

Opinions expressed by DZone contributors are their own.

Related

  • Demystifying Machine Learning: Unveiling Algorithms, Models, and Applications
  • How to Use Python for Data Science
  • Simple TensorFlow Model To Predict a Linear Regression
  • Linear Regression Model

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